refactor: splitting up of NonlinearSolve #229

Job	Run time
test (Core, lts, ubuntu-latest)	17s
test (Core, lts, macos-latest)	19s
test (Core, lts, windows-latest)	36s
test (Core, 1, ubuntu-latest)	49s
test (Core, 1, macos-latest)	35s
test (Core, 1, windows-latest)	1m 12s
test (Downstream, lts, ubuntu-latest)	22s
test (Downstream, lts, macos-latest)	20s
test (Downstream, lts, windows-latest)	43s
test (Downstream, 1, ubuntu-latest)	55s
test (Downstream, 1, macos-latest)	39s
test (Downstream, 1, windows-latest)	1m 9s
test (Misc, lts, ubuntu-latest)	30s
test (Misc, lts, macos-latest)	25s
test (Misc, lts, windows-latest)	33s
test (Misc, 1, ubuntu-latest)	46s
test (Misc, 1, macos-latest)	37s
test (Misc, 1, windows-latest)	1m 25s
test (Wrappers, lts, ubuntu-latest)	19s
test (Wrappers, lts, macos-latest)	18s
test (Wrappers, lts, windows-latest)	34s
test (Wrappers, 1, ubuntu-latest)	53s
test (Wrappers, 1, macos-latest)	37s
test (Wrappers, 1, windows-latest)	1m 40s
	16m 33s

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